Problem: Solve for $x$. $6x^2 + 60x + 150 = 0$ $x = $
Answer: Dividing both sides by $6$ gives: $ x^2 + {10}x + {25} = 0 $ The coefficient on the $x$ term is $10$ and the constant term is $25$, so we need to find two numbers that add up to $10$ and multiply to $25$. The number $5$ used twice satisfies both conditions: $ {5} + {5} = {10} $ $ {5} \times {5} = {25} $ So $(x + {5})^2 = 0$. $x + 5 = 0$ Thus, $x = -5$ is the solution.